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k a May Highlights and 2025 AoPS Online Class Information
jlacosta   0
May 1, 2025
May is an exciting month! National MATHCOUNTS is the second week of May in Washington D.C. and our Founder, Richard Rusczyk will be presenting a seminar, Preparing Strong Math Students for College and Careers, on May 11th.

Are you interested in working towards MATHCOUNTS and don’t know where to start? We have you covered! If you have taken Prealgebra, then you are ready for MATHCOUNTS/AMC 8 Basics. Already aiming for State or National MATHCOUNTS and harder AMC 8 problems? Then our MATHCOUNTS/AMC 8 Advanced course is for you.

Summer camps are starting next month at the Virtual Campus in math and language arts that are 2 - to 4 - weeks in duration. Spaces are still available - don’t miss your chance to have an enriching summer experience. There are middle and high school competition math camps as well as Math Beasts camps that review key topics coupled with fun explorations covering areas such as graph theory (Math Beasts Camp 6), cryptography (Math Beasts Camp 7-8), and topology (Math Beasts Camp 8-9)!

Be sure to mark your calendars for the following upcoming events:
[list][*]May 9th, 4:30pm PT/7:30pm ET, Casework 2: Overwhelming Evidence — A Text Adventure, a game where participants will work together to navigate the map, solve puzzles, and win! All are welcome.
[*]May 19th, 4:30pm PT/7:30pm ET, What's Next After Beast Academy?, designed for students finishing Beast Academy and ready for Prealgebra 1.
[*]May 20th, 4:00pm PT/7:00pm ET, Mathcamp 2025 Qualifying Quiz Part 1 Math Jam, Problems 1 to 4, join the Canada/USA Mathcamp staff for this exciting Math Jam, where they discuss solutions to Problems 1 to 4 of the 2025 Mathcamp Qualifying Quiz!
[*]May 21st, 4:00pm PT/7:00pm ET, Mathcamp 2025 Qualifying Quiz Part 2 Math Jam, Problems 5 and 6, Canada/USA Mathcamp staff will discuss solutions to Problems 5 and 6 of the 2025 Mathcamp Qualifying Quiz![/list]
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0 replies
jlacosta
May 1, 2025
0 replies
k i Adding contests to the Contest Collections
dcouchman   1
N Apr 5, 2023 by v_Enhance
Want to help AoPS remain a valuable Olympiad resource? Help us add contests to AoPS's Contest Collections.

Find instructions and a list of contests to add here: https://artofproblemsolving.com/community/c40244h1064480_contests_to_add
1 reply
dcouchman
Sep 9, 2019
v_Enhance
Apr 5, 2023
k i Zero tolerance
ZetaX   49
N May 4, 2019 by NoDealsHere
Source: Use your common sense! (enough is enough)
Some users don't want to learn, some other simply ignore advises.
But please follow the following guideline:


To make it short: ALWAYS USE YOUR COMMON SENSE IF POSTING!
If you don't have common sense, don't post.


More specifically:

For new threads:


a) Good, meaningful title:
The title has to say what the problem is about in best way possible.
If that title occured already, it's definitely bad. And contest names aren't good either.
That's in fact a requirement for being able to search old problems.

Examples:
Bad titles:
- "Hard"/"Medium"/"Easy" (if you find it so cool how hard/easy it is, tell it in the post and use a title that tells us the problem)
- "Number Theory" (hey guy, guess why this forum's named that way¿ and is it the only such problem on earth¿)
- "Fibonacci" (there are millions of Fibonacci problems out there, all posted and named the same...)
- "Chinese TST 2003" (does this say anything about the problem¿)
Good titles:
- "On divisors of a³+2b³+4c³-6abc"
- "Number of solutions to x²+y²=6z²"
- "Fibonacci numbers are never squares"


b) Use search function:
Before posting a "new" problem spend at least two, better five, minutes to look if this problem was posted before. If it was, don't repost it. If you have anything important to say on topic, post it in one of the older threads.
If the thread is locked cause of this, use search function.

Update (by Amir Hossein). The best way to search for two keywords in AoPS is to input
[code]+"first keyword" +"second keyword"[/code]
so that any post containing both strings "first word" and "second form".


c) Good problem statement:
Some recent really bad post was:
[quote]$lim_{n\to 1}^{+\infty}\frac{1}{n}-lnn$[/quote]
It contains no question and no answer.
If you do this, too, you are on the best way to get your thread deleted. Write everything clearly, define where your variables come from (and define the "natural" numbers if used). Additionally read your post at least twice before submitting. After you sent it, read it again and use the Edit-Button if necessary to correct errors.


For answers to already existing threads:


d) Of any interest and with content:
Don't post things that are more trivial than completely obvious. For example, if the question is to solve $x^{3}+y^{3}=z^{3}$, do not answer with "$x=y=z=0$ is a solution" only. Either you post any kind of proof or at least something unexpected (like "$x=1337, y=481, z=42$ is the smallest solution). Someone that does not see that $x=y=z=0$ is a solution of the above without your post is completely wrong here, this is an IMO-level forum.
Similar, posting "I have solved this problem" but not posting anything else is not welcome; it even looks that you just want to show off what a genius you are.

e) Well written and checked answers:
Like c) for new threads, check your solutions at least twice for mistakes. And after sending, read it again and use the Edit-Button if necessary to correct errors.



To repeat it: ALWAYS USE YOUR COMMON SENSE IF POSTING!


Everything definitely out of range of common sense will be locked or deleted (exept for new users having less than about 42 posts, they are newbies and need/get some time to learn).

The above rules will be applied from next monday (5. march of 2007).
Feel free to discuss on this here.
49 replies
ZetaX
Feb 27, 2007
NoDealsHere
May 4, 2019
Could I make AIME?
GallopingUnicorn45   85
N 8 minutes ago by BAM10
I'm a 4th grader, and I'm about half-way through Intro to Algebra, Intro to C&P, and Intro to Number Theory. I wouldn't say I get all of the material, but I understand like 80-90% of the material. Could I make AIME in 6th or 7th grade? Also, I'm doing AMC 8 for the second time, I got 15 questions last time, would I be able to make Honor or Distinguished Honor Roll this time?
85 replies
GallopingUnicorn45
Dec 11, 2024
BAM10
8 minutes ago
Resources for geometric/discrete probability
skronkmonster   2
N 15 minutes ago by skronkmonster
Hey everyone, was just looking for some good resources for geometric or discrete probability (situations where the set of successful/total outcomes can't be counted) because I'm having a lot of trouble understanding the chapter on geometric probability in the AoPS Intro to CP book. I couldn't find any great resources that were challenging enough online, so I thought maybe someone might have a suggestion. (Already tried Khan Academy but their material was either too advanced or too easy).

It looks like Richard has made a few videos about geometric probability, but not too many. Some additional resources and exercises would be nice, FYI--thanks in advance.
2 replies
skronkmonster
4 hours ago
skronkmonster
15 minutes ago
Easy Probability Question with sol
PikaVee   0
24 minutes ago
If there was a Pokemon battle where you had a Pikachu that was level 25 with only one move being Thunder with a 70% chance of hitting against a lv 28 1 HP Squirtle that has a 2 x weakness against Electric Type move and outspeeds your Pikachu with 4 total moves. Protect, Tackle, Water Gun and Rain Dance each with an equal chance of happening. The chances of it happening is a/b where a and b are coprime. What is ab?(Note: Only Protect can make the opposing Pokemon immune for one turn)


It is easier to find out the chances of the pokemon fainting in one turn than not so I will start with that. The chance of Pikachu using the move successfully is a 70% chance or $ \frac{7}{10} $ to hit and $ \frac{3}{4} $ that the opposing pokemon will use a not useful move. So $ \frac{7}{10}  *  \frac{3}{4} = \frac{21}{40} $ so the chances that the opposing pokemon will live for this turn is $1 -  \frac{21}{40} $ or $ \frac{19}{40} $. Now that we have a and b we multiply them and $19*40=760$


0 replies
1 viewing
PikaVee
24 minutes ago
0 replies
Geometry with fix circle
falantrng   33
N 2 hours ago by zuat.e
Source: RMM 2018 Problem 6
Fix a circle $\Gamma$, a line $\ell$ to tangent $\Gamma$, and another circle $\Omega$ disjoint from $\ell$ such that $\Gamma$ and $\Omega$ lie on opposite sides of $\ell$. The tangents to $\Gamma$ from a variable point $X$ on $\Omega$ meet $\ell$ at $Y$ and $Z$. Prove that, as $X$ varies over $\Omega$, the circumcircle of $XYZ$ is tangent to two fixed circles.
33 replies
1 viewing
falantrng
Feb 25, 2018
zuat.e
2 hours ago
USAMO 2001 Problem 2
MithsApprentice   54
N 2 hours ago by lpieleanu
Let $ABC$ be a triangle and let $\omega$ be its incircle. Denote by $D_1$ and $E_1$ the points where $\omega$ is tangent to sides $BC$ and $AC$, respectively. Denote by $D_2$ and $E_2$ the points on sides $BC$ and $AC$, respectively, such that $CD_2=BD_1$ and $CE_2=AE_1$, and denote by $P$ the point of intersection of segments $AD_2$ and $BE_2$. Circle $\omega$ intersects segment $AD_2$ at two points, the closer of which to the vertex $A$ is denoted by $Q$. Prove that $AQ=D_2P$.
54 replies
MithsApprentice
Sep 30, 2005
lpieleanu
2 hours ago
German-Style System of Equations
Primeniyazidayi   1
N 3 hours ago by Primeniyazidayi
Source: German MO 2025 11/12 Day 1 P1
Solve the system of equations in $\mathbb{R}$

\begin{align*}
\frac{a}{c} &= b-\sqrt{b}+c \\
\sqrt{\frac{a}{c}} &= \sqrt{b}+1 \\
\sqrt[4]{\frac{a}{c}} &=\sqrt[3]{b}-1
\end{align*}
1 reply
Primeniyazidayi
3 hours ago
Primeniyazidayi
3 hours ago
gcd nt from switzerland
AshAuktober   5
N 3 hours ago by Siddharthmaybe
Source: Swiss 2025 Second Round
Let $a, b$ be positive integers. Prove that the expression
\[\frac{\gcd(a+b,ab)}{\gcd(a,b)}\]is always a positive integer, and determine all possible values it can take.
5 replies
AshAuktober
4 hours ago
Siddharthmaybe
3 hours ago
Shortlist 2017/G1
fastlikearabbit   92
N 3 hours ago by Ilikeminecraft
Source: Shortlist 2017
Let $ABCDE$ be a convex pentagon such that $AB=BC=CD$, $\angle{EAB}=\angle{BCD}$, and $\angle{EDC}=\angle{CBA}$. Prove that the perpendicular line from $E$ to $BC$ and the line segments $AC$ and $BD$ are concurrent.
92 replies
fastlikearabbit
Jul 10, 2018
Ilikeminecraft
3 hours ago
polynomial division vs simplify
Miranda2829   3
N 3 hours ago by idk12345678
the question is

4x² - 4x +1 divide by 2x + 1 write in fraction format

the answer is 2x-3 + 4/2x+1

so my question is can we simiplfy this -4x with 2x become -2x

then answer 4x² -2x+1?

Im confused , when do usual fraction division we can simplify, but in above question doesn't seem to work.

many thanks
3 replies
Miranda2829
May 25, 2025
idk12345678
3 hours ago
set construction nt
top1vien   2
N 4 hours ago by top1vien
Is there a set of 2025 positive integers $S$ that satisfies: for all different $a,b,c,d\in S$, we have $\gcd(ab+1000,cd+1000)=1$?
2 replies
top1vien
Yesterday at 10:04 AM
top1vien
4 hours ago
strange geometry problem
Zavyk09   0
4 hours ago
Source: own
Let $ABC$ be a triangle with circumcenter $O$ and internal bisector $AD$. Let $AD$ cuts $(O)$ again at $M$ and $MO$ cuts $(O)$ again at $N$. Point $L$ lie on $AD$ such that $(AD, LM) = -1$. The line pass through $L$ and perpendicular to $AD$ intersects $NC, NB$ at $P, Q$ respectively. Let circumcircle of $\triangle NPQ$ cuts $(O)$ at $G \ne N$. Prove that $\angle AGD = 90^{\circ}$.
0 replies
Zavyk09
4 hours ago
0 replies
A sharp one with 3 var (3)
mihaig   3
N 4 hours ago by JARP091
Source: Own
Let $a,b,c\geq0$ satisfying
$$\left(a+b+c-2\right)^2+8\leq3\left(ab+bc+ca\right).$$Prove
$$a^2+b^2+c^2+5abc\geq8.$$
3 replies
mihaig
Yesterday at 5:17 PM
JARP091
4 hours ago
Dophantine equation
MENELAUSS   2
N 4 hours ago by Assassino9931
Solve for $x;y \in \mathbb{Z}$ the following equation :
$$3^x-8^y =2xy+1 $$
2 replies
MENELAUSS
Yesterday at 11:35 PM
Assassino9931
4 hours ago
Shortest number theory you might've seen in your life
AlperenINAN   9
N 4 hours ago by Assassino9931
Source: Turkey JBMO TST 2025 P4
Let $p$ and $q$ be prime numbers. Prove that if $pq(p+1)(q+1)+1$ is a perfect square, then $pq + 1$ is also a perfect square.
9 replies
AlperenINAN
May 11, 2025
Assassino9931
4 hours ago
k Series Question
Mathisfun04   17
N Aug 20, 2016 by RivuROX
What is the sum of the infinite series 1 + 2/3 + 4/9 + 8/27. . .?
17 replies
Mathisfun04
Jul 10, 2016
RivuROX
Aug 20, 2016
Series Question
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G H BBookmark kLocked kLocked NReply
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Mathisfun04
752 posts
#1 • 2 Y
Y by Adventure10, Mango247
What is the sum of the infinite series 1 + 2/3 + 4/9 + 8/27. . .?
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claserken
1772 posts
#2 • 4 Y
Y by Mathisfun04, blitzkrieg21, Adventure10, Mango247
$\boxed{3}$, how is this a MC Nats prob?
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First
2352 posts
#3 • 4 Y
Y by Mathisfun04, blitzkrieg21, Adventure10, Mango247
3, this problem is fairly trivial
Sniped
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mathguy5041
2659 posts
#4 • 2 Y
Y by Adventure10, Mango247
claserken wrote:
$\boxed{3}$, how is this a MC Nats prob?

This is a bit harder than most MC nats sprint 1s, don't you agree?
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claserken
1772 posts
#5 • 2 Y
Y by Adventure10, Mango247
mathguy5041 wrote:
claserken wrote:
$\boxed{3}$, how is this a MC Nats prob?

This is a bit harder than most MC nats sprint 1s, don't you agree?

I've never taken a MC Nat test before.
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TopNotchMath
1747 posts
#6 • 1 Y
Y by Adventure10
claserken wrote:
mathguy5041 wrote:
claserken wrote:
$\boxed{3}$, how is this a MC Nats prob?

This is a bit harder than most MC nats sprint 1s, don't you agree?

I've never taken a MC Nat test before.

MC Nat Sprint #1 are supposed to be of that material, a bit easy perhaps.
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asp211
2145 posts
#7 • 2 Y
Y by Adventure10, Mango247
it could be countdown
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hinna
974 posts
#8 • 4 Y
Y by The_Herring, Blue_Whale, Adventure10, Mango247
Well its 3. I guess I'll explain why:

This is a geometric series with common ratio $\frac {2}{3}$ and first term 1. To find the sum of an infinite geometric series with common term $r$ and 1st term $n$, we do $\frac {n}{1-r}$ and plugging the numbers in, we get $\frac {1}{1-\frac {2}{3}}=\boxed 3$.

The proof for the sum formula is that if you have $a_1, a_2, a_3...$ where each term is multiplied by a common factor. Then we write $a_1, ra_1, r^2a_1...=S$. Then $Sr=ra_1+r^2a_1...$ which means the sum times the common factor between two consecutive terms plus the first term equals the sum is : $S=a_1+Sr$. AKA simplifying, we get:
$S-Sr=a_1$
$S\cdot(1-r)=a_1$
$S=\frac {a_1}{1-r}$
This post has been edited 1 time. Last edited by hinna, Jul 10, 2016, 7:41 PM
Reason: Reason A
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blitzkrieg21
996 posts
#9 • 2 Y
Y by Adventure10, Mango247
Mathisfun04 wrote:
What is the sum of the infinite series 1 + 2/3 + 4/9 + 8/27. . .?

Solution
This post has been edited 1 time. Last edited by blitzkrieg21, Aug 19, 2016, 9:31 PM
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_--__--_
584 posts
#10 • 2 Y
Y by Adventure10, Mango247
@claserken

If you've never taken a MC Nats test before, then how could you possibly ask, "how is this a MC Nats prob?"

Also, using your logic, if I've never taken an AMC 12 test before, and I know that AMC 12 is harder than AMC 10, am I right to assume that there will be no simple questions on the AMC 12 at all?
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jack74
2319 posts
#11 • 1 Y
Y by Adventure10
There is no way that this is the sum. This may be the partial sum, but definitely not the real sum.
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_--__--_
584 posts
#12 • 2 Y
Y by Adventure10, Mango247
@jack74
If that's the case, then what is the "real sum"?
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william2001
110 posts
#13 • 2 Y
Y by Adventure10, Mango247
jack74 wrote:
There is no way that this is the sum. This may be the partial sum, but definitely not the real sum.

Your profile says that you are in elementary school, so I'll assume so. Maybe you have not learned this yet, but it is possible to sum up an infinite number of elements in a series with a common ratio less than 1. We say that the series converges to that number.
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StarFrost7
896 posts
#14 • 2 Y
Y by Adventure10, Mango247
jack74 wrote:
There is no way that this is the sum. This may be the partial sum, but definitely not the real sum.

You want proof? I'll give you proof. (Because everyone else hasn't hid their solutions, it's no use hiding mine.)

Note that we can assign the value $s$ to $1 + \dfrac23 + \dfrac49 + \cdots.$ We can factor out a term of $\dfrac23$ out of every term after $1:$

$$s = 1 + \dfrac23\left(1 + \dfrac23 +\dfrac49\right).$$
The expression in the parentheses is just $s$! For a finite series, this would be untrue. However, this is an infinite series. We can do things like this to them.

Now, just substitute:

$$s = 1+\dfrac23(s).$$
And solve:

$$\dfrac13(s) = 1.$$
Thus $\boxed{s=3.}$

If you still don't believe me, I'll give you a piece of very wise advice. Never, ever take calculus.
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Designerd
799 posts
#15 • 2 Y
Y by Adventure10, Mango247
jack74 wrote:
There is no way that this is the sum. This may be the partial sum, but definitely not the real sum.

What is real sum?
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Designerd
799 posts
#16 • 2 Y
Y by Adventure10, Mango247
Solution
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jeffisepic
1195 posts
#19 • 2 Y
Y by Adventure10, Mango247
trivial
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RivuROX
6 posts
#20 • 3 Y
Y by dragonmaster3000, Adventure10, Mango247
Mathisfun04 wrote:
What is the sum of the infinite series 1 + 2/3 + 4/9 + 8/27. . .?

3
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a